INTEREST RATES

Replicating Interest Rate Swaps with Eurodollar Strips

MAY 16, 2013 John W. Labuszewski

David Boberski

Daniel Grombacher

Managing Director

Managing Director

Senior Director

Research & Product Development

Research & Product Development

Research & Product Development

312-466-7469

212-299-2542

312-634-1583

[email protected]

[email protected]

[email protected]

The term “futurization” is being applied to describe the process through which trading and regulatory practices in exchange-traded futures and over-thecounter (OTC) derivative instruments are converging. This convergence is evident when we consider the impact of the Dodd-Frank financial reform legislation passed in 2010. Amongst other requirements, DoddFrank mandates centralized counterparty (CCP) clearing of certain types of standardized OTC swaps notably including “plain vanilla” interest rate swaps (IRS). Thus, we may plainly observe a convergence of OTC derivative markets with exchange traded futures where clearing has been the norm for over a century. But even before that, we note that CME Eurodollar futures and IRS markets meshed together quite nicely. Both markets were both introduced in the early 1980s and grew to achieve widespread acceptance by the institutional trading community. In the process, Eurodollar futures became commonly used as a pricing reference and hedging tool for IRS positions – an early manifestation of “futurization.” Specifically, Eurodollar futures may be deployed in the form of a “weighted strip” to replicate the performance of the floating rate payments associated with a plain vanilla swap, with some limitations as discussed below. While many IRS instruments will be subject to mandatory clearance moving forward, we note that the new regulatory framework provides exchangetraded futures with some capital efficiencies relative to OTC swaps. Thus, this article addresses the mechanics of replicating an IRS instrument with Eurodollar futures strips. We consider the construction of a strip; how one might price IRS by reference to Eurodollar futures values; and, how one might hedge or replicate the risks of an IRS with Eurodollar futures. We conclude with a review of the capital efficiencies associated with futures relative to cleared IRS. Eurodollar Futures Strips A Eurodollar futures strip may be bought or sold by buying or selling a series of futures maturing in successively deferred months, often in combination 1

with a cash investment in the near term. The initial cash investment is often referred to as the “front tail,” or “stub,” of the strip transaction. For example, assume it is December and one creates a 1-year strip by investing in a 3-month term instrument maturing in March. If you also purchase March, June and September Eurodollar futures, you effectively “lock-in” an investment return over each of the subsequent 3-month windows. This series of four (4) successive 3-month investments constitutes a synthetic 1-year investment, effectively locking in a 1-year rate of return. 1-Year Eurodollar Futures Strip Buy 3-Mth Term Investment

0

Buy Mar Futures

90

Buy Jun Futures

180

Buy Sep Futures

270

360

Timeline in Days

The value of a strip may be calculated as the compounded rate of return on the components of the strip as follows. 𝑛

𝑑𝑎𝑦𝑠𝑖 𝑡𝑒𝑟𝑚 �� − 1� ÷ � � 𝑆𝑡𝑟𝑖𝑝 = �� �1 + 𝑅𝑖 ∙ � 360 360 𝑖=1

Where Ri = rate associated with each successive period; daysi = number of days in each successive period; and, term = number of days associated with the cumulative period over which the strip extends. For example, let’s consider an approximate 2-year strip populated with actual market values. As of January 30, 2013, one might have created a strip by investing in a stub at a rate of 0.2265% and purchasing Mar-13, Jun-13, Sep-13, Dec-13, Mar14, Jun-14 and Sep 14 Eurodollar futures. The compound yield on the strip, as depicted in Table 1 below, was 0.408%. Investors often compare the value of “synthetic” investments created with Eurodollar futures strips to yields associated with comparable term investments in search of enhanced returns or “alpha.” Frequently these strips are spread vs. comparable term investments to capitalize on perceived mispricings.

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

One may compare the yield on a strip vs. the yield on comparable term Treasury securities. This is known as a “TED” or Treasury vs. Eurodollar spread. Eurodollars represent private credit risks while Treasuries reflect public credit risk or the “risk-free” rate. Compare strip yield to yields of comparable term securities



Buy “cheap” and sell “rich” instruments

We normally expect strips to generate higher returns than comparable maturity Treasuries. But when the relationship between these securities departs from normally expected patterns, one may buy the instrument considered “cheap” and sell the instrument that is “rich” as a form of arbitrage transaction. Packs and Bundles Because strips have proven to be popular trading instruments and because of the complexities associated with their purchase or sale, the exchange has developed the concept of “packs” and “bundles” to facilitate strip trading. A pack or bundle may be thought of as the purchase or sale of a series of Eurodollar futures representing a particular segment of the yield curve. Packs and bundles should be thought of as building blocks used to create or liquidate positions along various segments of interest along the yield curve. Packs and bundles may be bought or sold in a single transaction, eliminating the possibility that a multitude of orders in each individual contract goes unfilled. Note that the popularity of these concepts is reflected in Eurodollar volume and open interest patterns. Unlike most futures contracts, where virtually all volume and open interest is concentrated in the nearby or lead month, Eurodollar futures have significant volume and open interest in the deferred months going out 10 years along the yield curve. The exchange offers trading in 1-, 2-, 3-, 4-, 5-, 6-, 7-, 8-, 9-, and 10-year bundles. These products may be thought of as Eurodollar futures strips, absent the front tail or stub investment, extending out one to 10 years into the future. 2

Eurodollar futures are sometimes color coded such that the 1st 4 quarterlies are referred to as “whites,” the 2nd 4 as “reds,” the 3rd 4 as “greens,” etc. Thus, one might place an order by reference to the color code of the pack or bundle. For example, one may buy a 1-year or “white” bundle by purchasing the 1st 4 quarterly expiration Eurodollar futures contracts. Or, one may sell a “green” 3-year bundle by selling the 1st 12 quarterly expiration Eurodollar futures contracts. The price of a bundle is typically quoted by reference to the average change in the value of all Eurodollar futures contracts in the bundle since the prior day’s settlement price. For example, if the 1st 4 quarterly Eurodollar contracts are up 2 basis points for the day and the 2nd 4 quarterly Eurodollar contracts are up 3 basis points for the day, then the 2-year bundle may be quoted as + or up 2.5 basis points. After a trade is concluded at a negotiated price, prices are assigned to each of the various legs or Eurodollar futures associated with the bundle. These prices must be within the daily range for at least one of the component contracts of the bundle. This assignment is generally administered through an automated system operated by the exchange. Packs are similar to bundles in that they represent an aggregation of a number of Eurodollar futures contracts traded simultaneously. But they are constructed to represent a series of 4 consecutive quarterly Eurodollar futures. For example, one may buy a “white” pack by buying the 4 front contracts. Or, one may sell a “red” pack in the 2nd year by selling the 5th through 8th quarterly cycle month contracts. Packs are quoted and prices are assigned to the individual legs in the same manner that one quotes and assigns prices to the legs of a bundle. Interest Rate Swaps An interest rate swap is a financial transaction that entails multiple, periodic payments (swaps) of a sum determined by reference to a fixed rate of interest and payable by one swap counterparty; vs. a sum determined by reference to a floating or variable rate of interest and payable by the other counterparty. The fixed rate payer (floating rate

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

receiver) is generally referred to simply as the “payer” while the fixed rate receiver (floating rate payer) may be referred to simply as the “receiver.” Interest Rate Swap (IRS)

Fixed Rate Payer

Fixed Payments

Fixed Payments

Dealer Floating Payments

Floating Payments

Fixed Rate Receiver

For example, one may swap a quarterly payment based upon a specified fixed rate of interest, such as 1%, applied to a principal value of $10 million for the next 5 years; for a quarterly payment based upon 3-month LIBOR rates applied to a principal value of $10 million for the next 5 years. These periodic fixed vs. floating rate payments are typically netted such that only the net amount due is passed between payer and receiver. Clearly, the fixed rate payer hopes that floating rates rise such that his future receipts are increased. The floating rate payer, or fixed rate receiver, hopes that floating rates decline such that his future payments are diminished. Eurodollar & IRS Growth

$450

900

$400

800

$350

700

$300

600

$250

500

$200

400

$150

300 200

$100

100

$50 $0

Volume in CME Eurodollar products have grown on a strikingly parallel path along with over-the-counter swaps. This underscores the fact that Eurodollar futures and inextricably intertwined with the IRS market as a source for pricing and a tool to hedge the risks associated with swaps. In particular, banks and broker-dealers making a market in over-thecounter (OTC) swaps represent primary Eurodollar market participants. BBA LIBOR Swap The British Banker’s Association (BBA) LIBOR fixings represent a benchmark against which many interest rate products including CME Eurodollar futures and interest rate swaps routinely are pegged. Because of this focus on the BBA LIBOR fixing rate and the liquidity associated with Eurodollar futures, a particular type of IRS – a “BBA LIBOR Swap” – is frequently traded in the over-the-counter (OTC) markets. A BBA LIBOR Swap may be constructed to reference the 3-month BBA LIBOR fixing as the basis for the floating rate payments, frequently on the same dates as standard CME Eurodollar futures are settled (so-called “IMM dates”). As such, there is a closely compatible relationship between BBA LIBOR Swaps and CME Eurodollar futures that facilitates use of futures as a reference for pricing, and a tool for hedging, swaps. Further, this implies that futures may be used as a proxy to mimic the performance of a BBA LIBOR Swap, albeit with some qualifications. 2

1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011

0

Outstanding IRS (Trillions)

ED Volume (Mill Cnts)

1,000

IRS market has grown to some $379.4 trillion in outstanding notional value as of June 2012. 1

Eurodollars

IRS

The seminal interest rate swap transaction was concluded in 1980 while Eurodollar futures were originally introduced in 1981. Since that time the

3

1

2

As reported by the Bank of International Settlements (BIS) in its semi-annual survey of the over-the-counter (OTC) derivatives marketplace. Note that, unlike OTC swaps, CME Eurodollar futures do not exhibit convexity, or a non-linear relationship between price and yield. Rather, futures exhibit a linear relationship such that a one basis point (0.01%) change in yield uniformly represents a monetary change of $25.00 in the value of a single futures contract. This lack of convexity implies that one must adjust one’s Eurodollar position periodically in order to achieve a similar effect.

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

Pricing Swaps Interest rate swaps are typically quoted (on an opening basis) by reference to the fixed rate of interest. That fixed rate is calculated as the rate that renders equivalent the present value of the anticipated periodic fixed rate payments (PVfixed); with the present value of the anticipated periodic floating rate payments (PVfloating).

calculated as $76,934.49. The equivalence of these two cash flow streams may be established by reference to Table 5 found in the appendix. As such, this is a par swap that may be transacted with no up-front monetary consideration. 47 𝑅𝑓𝑖𝑥𝑒𝑑 = 4 ∙ ��0.9997 ∙ 0.002265 ∙ � �� 360

91 + �0.9989 ∙ 0.003000 ∙ � �� 360 91 + �0.9981 ∙ 0.003300 ∙ � �� 360 91 + �0.9972 ∙ 0.003650 ∙ � �� 360 91 + �0.9962 ∙ 0.004050 ∙ � �� 360 91 + �0.9950 ∙ 0.004500 ∙ � �� 360 91 + �0.9938 ∙ 0.005100 ∙ � �� 360 91 + �0.9923 ∙ 0.005800 ∙ � ��� 360 ÷ (0.9997 + 0.9989 + 0.9981 + 0.9972 + 0.9962 + 0.9950 + 0.9938 + 0.9923) = 0.3861%

Those floating rate payments may be estimated by examining the shape of the yield curve, or more practically, by referencing the rates associated with Eurodollar futures prices which reflect the shape of the curve. 𝑃𝑉𝐹𝑖𝑥𝑒𝑑 = 𝑃𝑉𝐹𝑙𝑜𝑎𝑡𝑖𝑛𝑔

When an IRS is transacted such that the present value of the estimated floating rate payments equals the present value of the fixed rate payments, no monetary consideration is passed on the basis of this initial transaction. This is also referred to as a “par swap.” In other words, the “non-par payment” (NPP) is set at zero ($0). 𝑁𝑃𝑃 = 0 = 𝑃𝑉𝐹𝑙𝑜𝑎𝑡𝑖𝑛𝑔 − 𝑃𝑉𝐹𝑖𝑥𝑒𝑑

The fixed rate (Rfixed) associated with a swap may be calculated by reference to the following formula.

𝑅𝑓𝑖𝑥𝑒𝑑 =

4 ∙ ∑𝑛𝑖=1 �𝑃𝑉𝑖 ∙ 𝑅𝑖 ∙ � ∑𝑛𝑖=1 𝑃𝑉𝑖

𝑑𝑎𝑦𝑠𝑖 360

��

Where PVi = present value discounting factor; Ri = rate associated with each successively deferred period; daysi = number of days in each successively deferred period. Note that those rates may be determined by reference to Eurodollar futures pricing. For example, find the value of a 2-year swap where the floating rate is estimated by reference to the BBA 3-month Eurodollar time deposit rate as of January 30, 2013. Table 4, found in the appendix below, provides details regarding the calculations. The fixed rate of interest associated with the swap may be calculated as 0.3861%. The present value of the fixed and floating rate payments given a fixed rate of 0.3861% may be 4

Note that, once transacted, an IRS might be rather unique to the extent that there are a plethora of variables associated with the transaction. These include features such as the specific floating reference rate, the periodic reset dates, the date conventions, etc. Because there are a large number of variable features associated with an IRS, the market for swaps is fragmented amongst many outstanding swaps with divergent contract terms and conditions. Because the swap market is rather fragmented, bilateral counterparties who wish to close or retire an outstanding swap transaction frequently must negotiate such a “close-out” or “tear-up” directly with the original counterparty. These closing transactions are typically quoted by reference to the non-par value of the swap at the time of such closeout. For example, interest rates may have advanced since the original transaction was concluded at a NPP=0. As such, the fixed rate payer is advantaged while the floating rate payer is disadvantaged. Thus, the floating rate payer may be required to compensate the fixed rate payer with a NPP that reflects the difference between the PVfloating and PVfixed per current market conditions.

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

For example, interest rates may have declined since the original transaction was concluded at a NPP=0. As such, the fixed rate payer is disadvantaged while the floating rate payer is advantaged. Thus, the fixed rate payer may be required to compensate the floating rate payer with a NPP that reflects the difference between the PVfloating and PVfixed per current market conditions. Hedging Swaps Just as interest rate swaps may be priced by reference to Eurodollar futures values, they may also be hedged with Eurodollar futures positions. This is, of course, facilitated to the extent that the swap is structured to parallel the characteristics of Eurodollar futures contracts. For example, basis risk is reduced to the extent that the floating rate associated with the swap is based on the same BBA 3-month Eurodollar time deposit rate that is used to cash-settle the futures contract, a “BBA swap.” Basis risk is further reduced to the extent that the swap is reset on dates corresponding to the quarterly expiration of the futures contracts. 3 As a general rule, the fixed rate payer is exposed to the risk of falling rates and rising prices. This suggests that fixed rate payers generally buy Eurodollar futures as a hedging strategy. Similarly, fixed rate receivers (floating rate payers) are exposed to the risk of rising rates and falling prices. Thus, fixed rate receivers may sell Eurodollar futures as a hedging strategy. Fixed rate payers exposed to risk of falling rates



Buy Eurodollar futures

Fixed rate receivers exposed to risk of rising rates



Sell Eurodollar futures

Just as we might identify the BPV of a loan instrument to assess the magnitude of risk, we might also calculate the BPV of a swap.

3

5

Eurodollar futures expire on the 2nd business day prior to the 3rd Wednesday of the contract month. These dates are referred to as “IMM dates” with a nod to the International Monetary Market or the nomenclature that was once associated with the division of the Chicago Mercantile Exchange on which financial products were traded. The reference endures even though the Exchange no longer categorizes its products into an IMM division.

Unfortunately, there is no simple, formula to reference in this regard. nonetheless estimate the BPV of comparing its non-par value given spaced 1 basis point apart.

deterministic But we may a swap by yield levels

For example, find the BPV of a 2-year IMM-dated swap with a $10 million notional amount, as discussed above. Note that the swap is originally transacted at par such that the PVfloating = PVfixed = $76,934.49. Thus, the original non-par payment, or difference between the present value of the fixed and floating payments, totaled zero (NPP = $0). Assume that yields advance by 1 basis point (0.01%) at all points on the yield curve. Per this scenario and as detailed in Table6, found in the appendix, PVfixed = $76,926.70 while PVfloating = $78,687.26. Thus, the non-par value of the swap increase from $0 to $1,760.56 (=$78,687.26 $76,926.70). For example, the fixed rate payer profits by $1,760.56 in the market or non-par value of the swap; the floating rate payer loses $1,760.56 in value. As such, the swap has a BPV=$1,760.56. This suggests that the swap may be hedged using 70 Eurodollar futures. 𝐻𝑅 = $1,760.56 ÷ $25 = 70 𝑐𝑜𝑛𝑡𝑟𝑎𝑐𝑡𝑠

But in which contract month should the hedge be placed? The short or floating rate payer might sell 70 futures in a nearby contract month if the yield curve were expected to flatten or invert. Or, one might sell 70 futures in a deferred month if the yield curve were expected to steepen. (The implications of a change in the shape of the yield curve are discussed in some detail above.) Structuring the IRS Hedge But a more precise hedge may be achieved if one were to sell futures in Eurodollar months that match the swap reset dates and risk exposures. This may be accomplished by comparing the PVfixed and PVfloating cash streams at each reset date. For example, in reference to the December 2013 payment date and as shown in Table 7 below, PVfloating – PVfixed = $9,200.50 - $9,624.42 = $423.92. Assuming a 1 basis point advance in

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

yields, the difference now becomes PVfloating – PVfixed = $9,451.73 - $9,623.57 = -$171.84. This suggests that the floating rate payer is exposed to a risk in December 2013 that may be quantified with a BPV = $252.08 (=-$423.92 less -$171.84). This further suggests that the floating rate payer may hedge that particular reset date by selling 10 Dec-13 Eurodollar futures. 𝐻𝑅 = $252.08 ÷ $25 = 10.1

Similarly, the floating rate payer might sell various amounts of Eurodollar futures in successively deferred months to hedge the risk of rising rates and falling prices as calculated in Table 7 below. Action Sell 10 Mar-13 futures Sell 10 Jun-13 futures Sell 10 Sep-13 futures Sell 10 Dec-13 futures Sell 10 Mar-14 futures Sell 10 Jun-14 futures Sell 10 Sep-14 futures Total 70 Contracts

This hedge is “self-liquidating” in the sense that every 3 months as the rate over the subsequent 3month period is established, the Eurodollar futures sold to hedge that specific risk are cash-settled. However, this does not imply that the hedge requires no maintenance. Convexity The BPV associated with Eurodollar futures is unchanging at $25/contract. However, like coupon bearing fixed income instruments, swaps experience “convexity.” For example, the responsiveness or BPV of the swap’s value fluctuates as yields rise and fall. Convexity generally increases as a function of the tenor of the swap. Thus, it is advisable periodically to quantify the swap structure and determine if the recommended hedge structure might have changed as a function of fluctuating rates and swap convexity. 4

4

6

The convexity associated with a strip of Eurodollar futures may be assessed using various electronic calculation tools. Please refer to the “EDS” functionality on the Bloomberg system. Note CME Group has also launched a new “Eurodollar Futures E-quivalents” tool

Margins per Dodd-Frank The Dodd-Frank Wall Street Reform and Consumer Production Act was endorsed by President Obama on July 21, 2010 (“Dodd-Frank bill” or “the Bill”). The Bill enacts sweeping reforms affecting the over-thecounter (“OTC”) derivatives markets and reverses the portion of the Commodity Futures Modernization Act (“CFMA”) of 2000 that had largely exempted OTC derivatives from significant regulatory oversight. The broad provisions of the Bill will be supported and implemented by myriad specific and detailed regulations currently under development by the two primary agencies, the Commodity Futures Trading Commission (“CFTC”) and the Securities Exchange Commission (“SEC”). It remains unclear exactly what will eventually emerge as the regulatory framework per which OTC derivatives will be regulated. But the picture is starting to come more clearly into focus. On November 8, 2011, the CFTC issued final rules pertaining to the general provisions and core principles of a Derivative Clearing Organization (“DCO”). In particular, these rules stipulate the performance bond (or “margin”) requirements for financial futures, centrally cleared swaps, and swaps that are not centrally cleared. According to Part 39, Subpart B, Section 39.13(2)(ii), which governs risk margin methodology and coverage, a derivatives clearing organization: “…shall use models that generate initial margin requirements sufficient to cover the derivatives clearing organization’s potential future exposures to clearing members based on price movements in the interval between the last collection of variation margin and the time within which the derivatives clearing organization estimates that it would be able to liquidate a defaulting clearing member’s positions (liquidation time); provided, however, that a derivatives clearing organization shall use: (A) A minimum liquidation time that is one day for futures and options;

which may be used to identify how one may construct a Eurodollar strip in replication of an IRS instrument. You can access this tool at www.cmegroup.com/edequivalents

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

(B) A minimum liquidation time that is one day for swaps on agricultural commodities, energy commodities, and metals; (C) A minimum liquidation time that is five days for all other swaps; or (D) Such longer liquidation time as is appropriate based on the specific characteristics of a particular product or portfolio; provided further that the Commission, by order, may establish shorter or longer liquidation times for particular products or portfolios.”

In short, under the new rules, market participants must post initial performance bonds to cover a oneday liquidation timetable for financial futures transactions, a 5-day liquidation timetable for centrally cleared financial swaps, and a 10-day liquidation timetable for non-centrally cleared financial swaps. With respect to non-cleared financial swaps, the 10day liquidation timetable is only proposed. These rules will mandate that previously uncleared, bilaterally executed, plain-vanilla financial swaps be cleared by a qualified central counterparty (“QCCP”) and become subject to a 5-day liquidation timetable. Margin requirements for standardized, liquid futures contracts, such as Eurodollars, will generally be less onerous than margins required for an analogous position in a cleared, plain vanilla interest rate swap. This is intuitive to the extent that IRS instruments are customized transactions which typically cannot be liquidated in times of market stress with equal facility to futures.

For example, the margin requirements for a structured 5-year Eurodollar futures strip that mimics a 5-year IRS results in 50% margin savings. The margin on a 10-year structured Eurodollar futures strip is estimated at 42% less than that of a comparable 10-year IRS. Concluding Note Business practices in the OTC derivatives and exchange traded futures markets are converging in a process often referred to as “futurization.” As evidence, consider that the Dodd-Frank financial reform bill mandated centralized counterparty clearing of standardized IRS instruments. Similarly, Eurodollar futures may be utilized to price and hedge and, to a degree, replicate the performance of IRS instruments. But futures offer significant capital efficiencies vis-à-vis comparable cleared over-the-counter IRS instruments. To learn more about this www.cmegroup.com/eurodollar.

Estimated Margin Requirements as % of Notional Value (As of December 2012)

Tenor 2-Year 5-Year 10-Year

Cleared IRS 0.420% 1.580% 3.250%

Equivalent ED Strip 0.255% 0.795% 1.895%

Margin Savings 39% 50% 42%

For example, the margin requirements for a structured 2-year Eurodollar futures strip that mimics a 2-year interest rate swap may be estimated as of December 2012 as 0.255% of notional value. By contrast, the margin requirements associated with a cleared 2-year interest rate swap are estimated at 0.420%. Thus, one may use Eurodollar strips to replicate a risk exposure that is similar to an IRS instrument with 39% margin savings. 7

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

product,

visit

Table 1: Find Value of Strip (As of 1/30/13)

Instrument Stub Investment Mar-13 Eurodollars Jun-13 Eurodollars Sep-13 Eurodollars Dec-13 Eurodollars Mar-14 Eurodollars Jun-14 Eurodollars Sep-14 Eurodollars

Expiration Date

Days

3/18/13 6/17/13 9/16/13 12/16/13 3/17/14 6/16/14 9/15/14 12/15/14

47 138 229 320 411 502 593 684

Day Span 47 91 91 91 91 91 91 91

Price

Rate (R)

99.7000 99.6700 99.6350 99.5950 99.5500 99.4900 99.4200

0.2265% 0.3000% 0.3300% 0.3650% 0.4050% 0.4500% 0.5100% 0.5800%

Compound Value (CV) 1.0003 1.0011 1.0019 1.0028 1.0038 1.0050 1.0063 1.0078

Strip Yield 0.226% 0.275% 0.297% 0.317% 0.336% 0.357% 0.381% 0.408%

Table 2: Find Swap Value (As of 1/30/13)

Instrument Stub Investment Mar-13 Eurodollars Jun-13 Eurodollars Sep-13 Eurodollars Dec-13 Eurodollars Mar-14 Eurodollars Jun-14 Eurodollars Sep-14 Eurodollars

8

Expiration Date

Days

3/18/13 6/17/13 9/16/13 12/16/13 3/17/14 6/16/14 9/15/14 12/15/14

47 138 229 320 411 502 593 684

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

Day Span 47 91 91 91 91 91 91 91

Price

Rate (R)

Compound Value (CV)

99.7000 99.6700 99.6350 99.5950 99.5500 99.4900 99.4200

0.2265% 0.3000% 0.3300% 0.3650% 0.4050% 0.4500% 0.5100% 0.5800%

1.0003 1.0011 1.0019 1.0028 1.0038 1.0050 1.0063 1.0078

Discount Factor (PV) (= 1/CV) 0.9997 0.9989 0.9981 0.9972 0.9962 0.9950 0.9938 0.9923

Table 3: Confirm Par Value (As of 1/30/13)

Payment Date

Fixed Payments

Discount Factor

PV of Fixed Payments

Floating Payments

Discount Factor

3/18/13 6/17/13 9/16/13 12/16/13 3/17/14 6/16/14 9/15/14 12/15/14

$9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50

0.9997 0.9989 0.9981 0.9972 0.9962 0.9950 0.9938 0.9923

$9,648.65 $9,641.34 $9,633.30 $9,624.42 $9,614.58 $9,603.66 $9,591.29 $9,577.25 $76,934.49

$2,957.08 $7,583.33 $8,341.67 $9,226.39 $10,237.50 $11,375.00 $12,891.67 $14,661.11

0.9997 0.9989 0.9981 0.9972 0.9962 0.9950 0.9938 0.9923

PV of Floating Payments $2,956.21 $7,575.35 $8,325.94 $9,200.50 $10,198.34 $11,318.61 $12,811.24 $14,548.32 $76,934.49

Table 4: Find BPV of Swap (As of 1/30/13)

9

Payment Date

Fixed Payments

Discount Factor

PV of Fixed Payments

Floating Payments

Discount Factor

3/18/13 6/17/13 9/16/13 12/16/13 3/17/14 6/16/14 9/15/14 12/15/14

$9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50 $9,651.50

0.9997 0.9989 0.9981 0.9971 0.9961 0.9949 0.9936 0.9921

$9,648.52 $9,640.97 $9,632.69 $9,623.57 $9,613.48 $9,602.32 $9,589.71 $9,575.43 $76,926.70

$2,957.08 $7,836.11 $8,594.44 $9,479.17 $10,490.28 $11,627.78 $13,144.44 $14,913.89

0.9997 0.9989 0.9981 0.9971 0.9961 0.9949 0.9936 0.9921

Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP

PV of Floating Payments $2,956.17 $7,827.56 $8,577.69 $9,451.73 $10,448.95 $11,568.52 $13,060.29 $14,796.34 $78,687.26

Table 5: Structuring Hedge (As of 1/30/13)

Payment Date 3/18/13 6/17/13 9/16/13 12/16/13 3/17/14 6/16/14 9/15/14 12/15/14

Original Scenario (1) PV of (2) PV of (3) Fixed – Fixed Floating Float (2-1) Payments Payments $9,648.65 $2,956.21 ($6,692.44) $9,641.34 $7,575.35 ($2,065.99) $9,633.30 $8,325.94 ($1,307.37) $9,624.42 $9,200.50 ($423.92) $9,614.58 $10,198.34 $583.75 $9,603.66 $11,318.61 $1,714.95 $9,591.29 $12,811.24 $3,219.95 $9,577.25 $14,548.32 $4,971.07 $76,934.49 $76,934.49 $0.00

Rates Increase 1 Basis Point (4) PV of (5) PV of (6) FixedFixed Floating Float (5-4) Payments Payments $9,648.52 $2,956.17 ($6,692.35) $9,640.97 $7,827.56 ($1,813.41) $9,632.69 $8,577.69 ($1,055.00) $9,623.57 $9,451.73 ($171.84) $9,613.48 $10,448.95 $835.47 $9,602.32 $11,568.52 $1,966.20 $9,589.71 $13,060.29 $3,470.58 $9,575.43 $14,796.34 $5,220.91 $76,926.70 $78,687.26 $1,760.56

Difference in Cash Flows $0.09 $252.58 $252.37 $252.08 $251.72 $251.25 $250.63 $249.84 $1,760.56

Hedge Ratio (HR) 0.0 10.1 10.1 10.1 10.1 10.1 10.0 10.0 70.4

Copyright 2013 CME Group All Rights Reserved. Futures trading is not suitable for all investors, and involves the risk of loss. Futures are a leveraged investment, and because only a percentage of a contract’s value is required to trade, it is possible to lose more than the amount of money deposited for a futures position. Therefore, traders should only use funds that they can afford to lose without affecting their lifestyles. And only a portion of those funds should be devoted to any one trade because they cannot expect to profit on every trade. All examples in this brochure are hypothetical situations, used for explanation purposes only, and should not be considered investment advice or the results of actual market experience. Swaps trading is not suitable for all investors, involves the risk of loss and should only be undertaken by investors who are ECPs within the meaning of Section 1(a)18 of the Commodity Exchange Act. Swaps are a leveraged investment, and because only a percentage of a contract’s value is required to trade, it is possible to lose more than the amount of money deposited for a swaps position. Therefore, traders should only use funds that they can afford to lose without affecting their lifestyles. And only a portion of those funds should be devoted to any one trade because they cannot expect to profit on every trade. CME Group is a trademark of CME Group Inc. The Globe logo, E-mini, Globex, CME and Chicago Mercantile Exchange are trademarks of Chicago Mercantile Exchange Inc. Chicago Board of Trade is a trademark of the Board of Trade of the City of Chicago, Inc. NYMEX is a trademark of the New York Mercantile Exchange, Inc. The information within this document has been compiled by CME Group for general purposes only and has not taken into account the specific situations of any recipients of the information. CME Group assumes no responsibility for any errors or omissions. Additionally, all examples contained herein are hypothetical situations, used for explanation purposes only, and should not be considered investment advice or the results of actual market experience. All matters pertaining to rules and specifications herein are made subject to and are superseded by official CME, NYMEX and CBOT rules. Current CME/CBOT/NYMEX rules should be consulted in all cases before taking any action.

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Replicating IRS with Eurodollar Strips | May 16, 2013 | © CME GROUP